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Permutations and piecewise-constant approximation of continuous functions of n variables

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Abstract

We consider the problem of approximation of a continuous function f given on an n-dirnensional cube by step functions in the metrics of C and L p. We obtain exact error estimates in terms of the modulus of continuity of the function f or a special permutation of it.

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References

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    N. P. Korneichuk

Authors
  1. N. P. Korneichuk
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 907–918, July, 1998.

This work was partially supported by the International Soros Foundation for Support of Education Programs in the Natural Sciences (ISSEP) (grant No. EPU051030).

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Korneichuk, N.P. Permutations and piecewise-constant approximation of continuous functions of n variables. Ukr Math J 50, 1031–1044 (1998). https://doi.org/10.1007/BF02528832

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  • DOI: https://doi.org/10.1007/BF02528832

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